Some general problems on the number of parts in partitions
Compositions with distinct parts.
On the transformation equation for the partition generating function.
On partitions of N into summands coprime to N.
On partitions of N into summands coprime to N. (Short Communication).
On the transformation equation for the partition generating function (Short Communication).
An optimal search strategy based on user preferences for choice oriented databases
Growth of the product
We estimate the maximum of on the unit circle where 1 ≤ a₁ ≤ a₂ ≤ ... is a sequence of integers. We show that when is or when is a quadratic in j that takes on positive integer values, the maximum grows as exp(cn), where c is a positive constant. This complements results of Sudler and Wright that show exponential growth when is j. In contrast we show, under fairly general conditions, that the maximum is less than , where r is an arbitrary positive number. One consequence is that the...
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